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On a reliable solution of a Volterra integral equation in a Hilbert space. (English) Zbl 1099.45001

Summary: We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to a quasistationary problem for an anisotropic viscoelastic body made of a long memory material.

MSC:

45D05 Volterra integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
49J22 Optimal control problems with integral equations (existence) (MSC2000)
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References:

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